The feasibility of using the detection of electron antineutrinos produced in fission to monitor the time dependence of the plutonium content of nuclear power reactors is discussed. If practical, such a scheme would allow worldwide, automated monitoring of reactors and, thereby, the detection of certain proliferation scenarios. For GW(electric) power reactors, the count rates and the sensitivity of the antineutrino spectrum (to the core burnup) suggest that monitoring of the gross operational status of the reactor from outside the containment vessel is feasible. As the plutonium content builds up in a given burn cycle, the total number of antineutrinos steadily drops; and this variation is quite detectable, assuming fixed reactor power. The average antineutrino energy also steadily drops, and a measurement of this variation would be very useful to help offset uncertainties in the total reactor power. However, the expected change in the antineutrino signal from the diversion of a significant quantity of plutonium, which would typically require the diversion of as little as a single fuel assembly in a GW(electric) reactor, would be very difficult to detect.